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Beliebt Rechnen >

derivative of (3x-x^2/(sqrt(x))-4cot(x))

Lösung

\frac{d}{d x} (\frac{3 x - x ^{2}}{x} - 4 cot (x))

Lösung

\frac{3 - 3 x}{2 x} + 4 csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - x ^{2}}{x} - 4 cot (x))

Vereinfache

\frac{3 x - x ^{2}}{x} - 4 cot (x) : x (3 - x) - 4 cot (x)

= \frac{d}{d x} (x (3 - x) - 4 cot (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x (3 - x)) - \frac{d}{d x} (4 cot (x))

\frac{d}{d x} (x (3 - x)) = \frac{3 - 3 x}{2 x}

\frac{d}{d x} (4 cot (x)) = - 4 csc^{2} (x)

= \frac{3 - 3 x}{2 x} - (- 4 csc^{2} (x))

Vereinfache

= \frac{3 - 3 x}{2 x} + 4 csc^{2} (x)

Graph

Beliebte Beispiele

integral from-infinity to 0 of 1/(2-10x)

\int_{- \infty}^{0} \frac{1}{2 - 10 x} d x

(x^2sin(x)+4y)dx+xdy=0

(x^{2} sin (x) + 4 y) d x + x d y = 0

derivative of 3^{sqrt(x^2-1)}

\frac{d}{d x} (3^{x^{2} - 1})

derivative of at^5-5bt^3

\frac{d}{d x} (a t^{5} - 5 b t^{3})

limit as x approaches-2-of sqrt(2x+4)-2

x \to - 2 - lim (2 x + 4 - 2)